{"id":14763,"date":"2017-06-24T11:42:24","date_gmt":"2017-06-24T11:42:24","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=14763"},"modified":"2022-10-25T12:16:00","modified_gmt":"2022-10-25T12:16:00","slug":"two-phase-fluid-flow","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/","title":{"rendered":"Two-phase Fluid Flow"},"content":{"rendered":"<div   id="8n9s8rpp6h"    class=\"su-quote su-quote-style-default\"><div   id="8n9s8rpp6h"    class=\"su-quote-inner su-u-clearfix su-u-trim\"><b>Two<\/b>&#8211;<b>phase flow<\/b> is the interactive flow of <strong>two <\/strong>distinct phases with common interfaces in, say, a conduit. The <strong>most common<\/strong> being the simultaneous flow of <strong>steam and liquid water<\/strong> (as encountered in <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\"><strong>steam generators<\/strong> <\/a>and <strong>condensers<\/strong>).<\/div><\/div>\n<p>By definition, <strong>multiphase flow<\/strong> is the interactive flow of <strong>two or more<\/strong> distinct phases with common interfaces in, say, a conduit. Each phase, representing a volume fraction (or mass fraction) of solid, liquid, or ga搜索引擎优化us matter, has its <strong>own<\/strong> properties, <strong>velocity<\/strong>, and <strong>temperature<\/strong>.<\/p>\n<p>A multiphase flow can be a simultaneous flow of:<\/p>\n<ul>\n<li>Materials with <strong>different states or phases<\/strong> (e.g.,, water-steam mixture).<\/li>\n<li>Materials with <strong>different chemical properties<\/strong> but in the same state or phase (e.g.,, oil droplets in water).<\/li>\n<\/ul>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-fluid-flow.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-14768\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-fluid-flow.png\" alt=\"two-phase fluid flow\" width=\"82\" height=\"332\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-fluid-flow.png 82w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-fluid-flow-74x300.png 74w\" sizes=\"(max-width: 82px) 100vw, 82px\" \/><\/a>There are\u00a0many combinations in industrial processes, but the <strong>most common<\/strong> being the simultaneous flow of <strong>steam and liquid water<\/strong> (as encountered in <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\"><strong>steam generators<\/strong> <\/a>and <strong>condensers<\/strong>). In reactor engineering, a great deal of study has been performed on the nature of <strong>two-phase flow<\/strong> in case of a loss-of-coolant accident (<strong>LOCA<\/strong>), an accident of importance in reactor safety, and all thermal-hydraulic analyses (<strong>DNBR analyses<\/strong>).<\/p>\n<h2>Characteristics of Two-phase Fluid Flow<\/h2>\n<p>All two-phase flow problems have features that are characteristically different from those found in single-phase problems.<\/p>\n<ul>\n<li>In the case of steam and liquid water, the <strong>density<\/strong> of the two phases <strong>differs by a factor of about 1000<\/strong>. Therefore the influence of gravitational body force on multiphase flows is of much greater importance than in the case of single-phase flows.<\/li>\n<li>The <strong>sound speed<\/strong> changes dramatically for materials undergoing a phase change and can be orders of magnitude different. This significantly influences a <strong>flow through an orifice<\/strong>.<\/li>\n<li>The relative <strong>concentration<\/strong> of different phases is usually a dependent parameter of great importance in multiphase flows, while it is a parameter of no consequence in single-phase flows.<\/li>\n<li>The phase change means flow-induced pressure drops can cause further phase change (e.g.,, water can evaporate through an orifice), increasing the relative volume of the ga搜索引擎优化us, compressible medium and increasing efflux velocities, unlike single-phase incompressible flow where decreasing of an orifice would decrease efflux velocities.<\/li>\n<li>The spatial distribution of the various phases in the flow channel strongly affects the flow behavior.<\/li>\n<li>There are many types of instabilities in multiphase flow.<\/li>\n<\/ul>\n<h2>Basic Parameters of Two\u2010phase Fluid Flow<\/h2>\n<p>This section will consider the simultaneous flow of<strong> gas (or vapor) and liquid water<\/strong> (as encountered in <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\">steam generators <\/a>and condensers) in concurrent flow through a duct with cross-sectional area A. The subscripts <strong>\u201cv\u201d<\/strong> and<strong> \u201c\u2113\u201d<\/strong> indicate the <strong>vapor<\/strong> and <strong>liquid<\/strong> phase, respectively. Fundamental parameters that characterize this flow are:<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Void Fraction<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>The void fraction, \u03b1<\/strong>, is one of the most important parameters used to characterize two-phase fluid flow, especially the gas-liquid flow.<br \/>\nVarious geometric definitions are used for specifying this parameter. The void fraction in a two-phase fluid flow may be defined as:<\/p>\n<ol>\n<li>The fraction of the <strong>channel volume<\/strong> that is occupied by the gas phase. This void fraction is known as the <strong>volumetric void fraction.<\/strong><\/li>\n<li>The fraction of the <strong>channel cross-sectional area<\/strong> that is occupied by the gas phase. This void fraction is known as the <strong>cross-sectional void fraction<\/strong>.<\/li>\n<li>The <strong>local void fraction<\/strong> refers to that at one single point or very small volume. Therefore it takes the values of 1 or 0.<\/li>\n<\/ol>\n<p>For further purposes, we will assume a void fraction to be the fraction of the <strong>channel cross-sectional area<\/strong> that is occupied by the gas phase (i.e., cross-sectional void fraction) defined as:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/void-fraction-definition.png\"><img loading=\"lazy\" class=\" size-full wp-image-14771 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/void-fraction-definition.png\" alt=\"void fraction definition\" width=\"184\" height=\"98\" \/><\/a><br \/>\nThe void fraction is important in the two-phase flow because it influences key physical parameters, such as <strong>viscosity<\/strong>, <strong>pressure drop,<\/strong> and <strong>heat transfer<\/strong>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Static Quality<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In general, <strong>vapour quality<\/strong> is the mass fraction of vapour in a saturated mixture. Saturated vapor has a quality of 100%, and saturated liquid has a quality of 0%.<br \/>\nThe static quality in a two-phase fluid flow is defined as:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/static-quality-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14772\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/static-quality-definition.png\" alt=\"static quality - definition\" width=\"442\" height=\"97\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/static-quality-definition.png 442w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/static-quality-definition-300x66.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Flow Quality<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In two-phase fluid flow, it is convenient to use the <strong>flow quality<\/strong> instead of the static quality. The flow quality in a two-phase fluid flow is defined as:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-quality-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14773\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-quality-definition.png\" alt=\"flow quality - definition\" width=\"460\" height=\"102\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-quality-definition.png 460w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-quality-definition-300x67.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Mixture Density<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In two-phase fluid flow in is convenient to use the <strong>mixture density<\/strong>. The mixture density of the two-phase flow is used to calculate <strong>pressure drop<\/strong>. The mixture density in a two-phase fluid flow is defined as:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14774\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition.png\" alt=\"mixture density - definition\" width=\"312\" height=\"51\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition.png 312w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition-300x49.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Slip Ratio - Velocity ratio<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In two-phase fluid flow it is convenient to use the <strong>slip ratio<\/strong>. <strong>The slip ratio<\/strong> (or <strong>velocity ratio<\/strong>) in a two-phase flow is defined as the ratio of the velocity of the vapor phase to the velocity of the liquid phase. The slip ratio in a two-phase fluid flow is defined as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/slip-ratio-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14775\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/slip-ratio-definition.png\" alt=\"slip ratio - definition\" width=\"353\" height=\"385\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/slip-ratio-definition.png 353w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/slip-ratio-definition-275x300.png 275w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><\/a><\/p>\n<figure id=\"attachment_14781\" aria-describedby=\"caption-attachment-14781\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chart-Slip-Ratio.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14781\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chart-Slip-Ratio-300x241.png\" alt=\"Effect of S on \u03b1 vs x for water at 7 MPa. Source: Buongiorno Jacopo, MIT Department of Nuclear Science and Engineering, NOTES ON TWO-PHASE FLOW\" width=\"300\" height=\"241\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chart-Slip-Ratio-300x241.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chart-Slip-Ratio-177x142.png 177w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chart-Slip-Ratio-147x118.png 147w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chart-Slip-Ratio.png 601w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14781\" class=\"wp-caption-text\">Effect of S on \u03b1 vs. x for water at 7 MPa. Source: Buongiorno Jacopo, MIT Department of Nuclear Science and Engineering, NOTES ON TWO-PHASE FLOW<\/figcaption><\/figure>\n<p>In the <strong>homogeneous equilibrium model (HEM)<\/strong> of two-phase flow, the slip ratio is by definition assumed to be unity (there is no slip). However, most industrial two-phase flows have a different velocity of the gas and liquid phases. These can differ significantly. The models that account for the existence of the slip are called <strong>separated flow models<\/strong>.<\/p>\n<p>The relations between <strong>x, \u03b1, and S<\/strong> can be deducted, and the result is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/relations-between-quality-void-fraction-and-slip.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14782\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/relations-between-quality-void-fraction-and-slip.png\" alt=\"relations between quality, void fraction and slip\" width=\"619\" height=\"101\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/relations-between-quality-void-fraction-and-slip.png 619w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/relations-between-quality-void-fraction-and-slip-300x49.png 300w\" sizes=\"(max-width: 619px) 100vw, 619px\" \/><\/a><\/p>\n<p>The reason for defining the <strong>void fraction<\/strong> and the <strong>slip ratio<\/strong> is that they also make it possible to calculate the <strong>pressure drop<\/strong> of the two-phase flow. Several correlations for calculating the slip ratio, S, and the void fraction are presented in the literature. The following correlations are given in order of increasing accuracy.<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/smith-void-correlation.png\"><br \/>\n<\/a><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/homogeneous-flow-model.png\"><img loading=\"lazy\" class=\" size-full wp-image-14776 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/homogeneous-flow-model.png\" alt=\"homogeneous flow model\" width=\"191\" height=\"66\" \/><\/a><br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Zivi-slip-correlation.png\"><img loading=\"lazy\" class=\" size-full wp-image-14777 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Zivi-slip-correlation.png\" alt=\"Zivi slip correlation\" width=\"169\" height=\"94\" \/><\/a><br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chisholm-slip-correlation.png\"><img loading=\"lazy\" class=\" size-full wp-image-14778 aligncenter\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Chisholm-slip-correlation.png\" alt=\"Chisholm slip correlation\" width=\"207\" height=\"105\" \/><\/a><br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/smith-void-correlation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14779\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/smith-void-correlation.png\" alt=\"smith void correlation\" width=\"457\" height=\"154\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/smith-void-correlation.png 457w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/smith-void-correlation-300x101.png 300w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><\/a><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Superficial velocity<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Superficial velocity<\/strong> is a hypothetical flow velocity calculated as if the given phase or fluid were the <strong>only one flowing<\/strong> or present in a given cross-sectional area. The velocity of the given phase is calculated as if the second phase was ignored.<\/p>\n<p>In engineering multiphase flows and flows in porous media, <strong>superficial velocity<\/strong> is commonly used because it is an unambiguous value. In contrast, real velocity is often spatially dependent and subject to many assumptions.<\/p>\n<p>Superficial velocity can be expressed as:<br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/superficial-velocity-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14783\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/superficial-velocity-definition.png\" alt=\"superficial velocity - definition\" width=\"332\" height=\"196\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/superficial-velocity-definition.png 332w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/superficial-velocity-definition-300x177.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><\/a><\/p>\n<p>For better understanding, let us consider a pipe with a 0.1 m<sup>2<\/sup> cross-section of flow area. Assume that the flow rate is 1 m<sup>3<\/sup>\/s. For<strong> single-phase fluid flow,<\/strong> the <strong>superficial velocity will be equal to real fluid<\/strong> <strong>velocity,<\/strong> which will be 10 m\/s.<br \/>\nFor t<strong>wo-phase fluid flow<\/strong> (e.g.,, vapor-liquid flow), the situation will be different. Assuming the slip ratio is unity, both phases have taken separately, will have superficial velocities of <strong>5 m\/s<\/strong>. The resulting real velocity will then be equal to <strong>10 m\/s<\/strong>. If the two phases have different velocities (with slip), the situation will be more complicated.<\/div><\/div><\/div>\n<div   id="8n9s8rpp6h"    class=\"collapsible-container\">\n<h2>Flow Patterns &#8211; Two-phase Flow<\/h2>\n<p>One of the most challenging aspects of dealing with the <strong>two-phase flow or multiphase flow<\/strong> is the fact that it can take <strong>many different forms<\/strong>. <strong>Spatial distributions and velocities<\/strong> of the <strong>liquid and vapor phases<\/strong> in the flow channel are very important aspects in many engineering branches. <strong>Pressure drops<\/strong> and <strong>heat transfer coefficients<\/strong> strongly depend on the <strong>local flow structure,<\/strong> and thus it is important in the engineering of <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\"><strong>nuclear reactors<\/strong><\/a>. The observed flow structures are defined as <strong>two-phase flow patterns,<\/strong> and these have particular identifying characteristics. These different flow patterns have been <strong>categorized<\/strong> according to the <strong>direction of flow<\/strong> relative to gravitational acceleration.<\/p>\n<ul>\n<li><strong>Flow patterns in vertical tubes<\/strong><\/li>\n<li><strong>Flow patterns in horizontal tubes<\/strong><\/li>\n<\/ul>\n<figure id=\"attachment_14848\" aria-describedby=\"caption-attachment-14848\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-table.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14848\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-table-300x198.png\" alt=\"flow patterns\" width=\"300\" height=\"198\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-table-300x198.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-table.png 468w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14848\" class=\"wp-caption-text\">Table of basic flow patterns in vertical tubes.<\/figcaption><\/figure>\n<p>The main flow regimes <strong>in vertical tubes<\/strong> are shown in the table. It must be noted values of <a title=\"Static Quality \u2013 Flow Quality\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/static-quality-flow-quality\/\"><strong>flow quality<\/strong>\u00a0<\/a>and <strong>flow rate<\/strong> is dependent on the fluid and pressure. <strong>In horizontal tubes<\/strong>, there can also be <strong>stratified flow<\/strong> (especially at low flow rates), at which the two phases <strong>separate<\/strong> under the effect of gravity.<\/p>\n<p>The vapor\/gas phase tends to be distributed as <strong>small bubbles<\/strong> at low vapor flow rates for a constant liquid flow rate. <strong>Increasing void fraction<\/strong> causes the <strong>agglomeration<\/strong> of bubbles into <strong>larger plugs and slugs<\/strong>. Further agglomeration of slugs, caused by further <strong>increasing void fraction,<\/strong> causes separation of the phases into <strong>annular patterns<\/strong> wherein liquid concentrates at the channel wall, and <strong>vapor flows in the central core<\/strong> of the vertical channel.<\/p>\n<p><strong>For horizontal channels<\/strong>, gravitational force tends to drain the liquid annulus toward the bottom of the channel, resulting in <strong>stratified flow<\/strong>. The gravitational force acting on the liquid phase can be overcome by kinetic forces at high flow rates, causing stratified flows to revert to annular flows. <strong>At very high flow rates<\/strong>, the annular film is thinned by the shear of the vapor core, and all the liquid is entrained as droplets in the vapor phase. This flow regime is usually known as the <strong>mist flow<\/strong>.<\/p>\n<p>See also:\u00a0<strong>Engineering Data Book III, Thome, J.R., Wolverine Tube Inc, 2004.<\/strong><\/p>\n<h2>Flow Patterns &#8211; Vertical Tubes<\/h2>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Bubbly flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In the bubbly flow, the liquid flow rate is high enough to break up the gas into bubbles, but it is not high enough to cause the bubbles to become mixed well within the liquid phase. The <strong>bubbles vary widely in size and shape<\/strong>, but most commonly, they are nearly spherical and are much <strong>smaller than the diameter<\/strong> of the tube.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Slug flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Increasing void fraction<\/strong> causes <strong>agglomeration of bubbles<\/strong> into <strong>larger plugs and slugs<\/strong>. These slugs are similar in dimension to the tube diameter. These slugs travel at a speed that is a substantial fraction of the gas velocity and occur intermittently. Since these large gas slugs are separated from one another by slugs of liquid, they cause <strong>enormous pressure and liquid flow rate fluctuations<\/strong>. In some cases, a downward flow can be observed near the tube wall, even though the net flow of fluid is upward. The gravitational force causes this.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Churn flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Churn flow<\/strong>, also referred to as <strong>froth flow<\/strong> is a highly disturbed flow of two-phase fluid flow. The increasing velocity of a slug flow causes the structure of the flow to become <strong>unstable<\/strong>. The churn flow is characterized by a <strong>very thick and unstable liquid film<\/strong>, with the liquid often <strong>oscillating up and down<\/strong>. Due to its nearly <strong>chaotic properties<\/strong>, it is one of the least understood gas-liquid flow regimes.<\/p>\n<p>A typical example of churn flow is boiling flow in <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\"><strong>nuclear reactors<\/strong><\/a> during accidents. Especially for many accident scenarios, boiling may lead to a <strong>high void fraction,<\/strong> including <strong>churn-turbulent flow<\/strong>. Its flow structure and induced pressure changes may have a strong impact on safety.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Annular flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Annular flow<\/strong> is a flow regime of two-phase gas-liquid flow. It is characterized by the presence of a <strong>liquid film flowing on the channel wall<\/strong> (forming an annular ring of liquid) while the <strong>gas flows<\/strong> as a continuous phase up <strong>in the center of the tube<\/strong>. The flow core can contain entrained liquid droplets. The velocity of the gas core is very large, and it is large enough to cause high-frequency waves and ripples at the interface. This flow regime is particularly stable, and it is desired flow regime for high-velocity, high-quality two-phase fluid flow.<\/p>\n<p>Both adiabatic annular flows (without heat exchange) and diabatic annular flows (with heat exchange) occur in industrial applications:<\/p>\n<ul>\n<li><strong>in <a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\">steam generators<\/a><\/strong><\/li>\n<li><strong>condensers<\/strong><\/li>\n<li><a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\"><strong>boiling water reactors &#8211; BWR<\/strong><\/a><\/li>\n<li><strong>during accidents in<a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\"> PWRs<\/a><\/strong><\/li>\n<\/ul>\n<figure id=\"attachment_14791\" aria-describedby=\"caption-attachment-14791\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Churn-Annular-Mist-Flow.png\"><img loading=\"lazy\" class=\"wp-image-14791 size-medium\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Churn-Annular-Mist-Flow-300x191.png\" alt=\"Bubbly - Slug - Churn - Annular - Mist - Flow\" width=\"300\" height=\"191\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Churn-Annular-Mist-Flow-300x191.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Churn-Annular-Mist-Flow-460x295.png 460w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Churn-Annular-Mist-Flow.png 518w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14791\" class=\"wp-caption-text\">Sketches of flow regimes for two-phase flow in a vertical pipe. Source: Weisman, J. Two-phase flow patterns. Chapter 15 in Handbook of Fluids in Motion, Cheremisinoff N.P., Gupta R. 1983, Ann Arbor Science Publishers.<\/figcaption><\/figure>\n<p>In the case of <strong>BWR<\/strong>, in which a <strong>phase transition<\/strong> (evaporation) occurs, detailed knowledge of this flow regime is highly important. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the <strong>liquid wall film may exhaust,<\/strong> and the wall may be <strong>dried out<\/strong>. This phenomenon is usually known as <strong>\u201cdry out\u201d<\/strong>. <strong>Dryout<\/strong> is accompanied by a <strong>rapid rise in wall temperature<\/strong> and is important in the safety of BWRs.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Mist flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Mist flow<\/strong> is a flow regime of two-phase gas-liquid flow. It occurs at <strong>very high flow rates<\/strong> and <strong>very high flow quality<\/strong>. This condition causes the liquid film flowing on the channel wall to be thinned by the shear of the gas core on the interface until it becomes unstable and is destroyed. The flow core in the mist flow entrains <strong>all the liquid as droplets<\/strong> in the gas phase. Droplets may wet the tube wall, but this occurs <strong>intermittently<\/strong> and only <strong>locally<\/strong>. In the heated channel, the presence of a mist flow regime is accompanied with significantly higher wall temperatures and high fluctuation of wall temperatures.<\/div><\/div>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_14788\" aria-describedby=\"caption-attachment-14788\" style=\"width: 418px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-vertical-flow-Hewitt.png\"><img loading=\"lazy\" class=\"wp-image-14788 size-full\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-vertical-flow-Hewitt.png\" alt=\"flow patterns - vertical flow - Hewitt\" width=\"428\" height=\"397\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-vertical-flow-Hewitt.png 428w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-vertical-flow-Hewitt-300x278.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/a><figcaption id=\"caption-attachment-14788\" class=\"wp-caption-text\">The vertical flow regime map of Hewitt and Roberts (1969) for flow in a 3.2cm diameter tube, validated for both air\/water flow at atmospheric pressure and steam\/water flow at high pressure. Source: Brennen, C.E., Fundamentals of Multiphase Flows, Cambridge University Press, 2005, ISBN 0521 848040<\/figcaption><\/figure>\n<h2>Flow Patterns &#8211; Horizontal Tubes<\/h2>\n<div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Bubbly flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In contrast to the bubbly flow in the vertical channel, the bubbly flow in the horizontal channel is <strong>strongly influenced by gravitational force<\/strong>. Due to the <strong>buoyancy<\/strong>, bubbles are dispersed in the liquid with a higher concentration in the upper half of the channel. This regime typically occurs at <strong>higher flow rates<\/strong> because, at lower flow rates, the gravitational force tends to drain the liquid annulus toward the bottom of the channel, resulting in <strong>stratified flow<\/strong>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Stratified flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In two-phase fluid flow, the <strong>gravitational force plays a very important role<\/strong> because the fluid with lower density (e.g.,, gas) is always above the fluid with higher density. <strong>Stratified flows<\/strong> are <strong>very common in nature<\/strong>, for example, in the ocean and the atmosphere. In the internal flows, the stratified flow occurs at <strong>low liquid and gas velocities<\/strong>. As the velocity of the gas increases, the horizontal interface becomes more disturbed, and waves may be formed. This flow regime is usually known as the <strong>stratified-wavy flow<\/strong>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Plug flow and Slug flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Further increase in the gas velocity causes that <strong>waves reach the top of the tube<\/strong>. Whether the flow will be plug or slug flow depends especially on the void fraction that causes agglomeration of bubbles into larger plugs and slugs. In the plug flow, the diameters of the bubbles are smaller than the tube. Slugs are similar in dimension to the tube diameter. The slugs travel at a speed that is a substantial fraction of the gas velocity and occur intermittently. Since these large gas slugs are separated from one another by slugs of liquid, they cause <strong>large pressure and liquid flow rate fluctuations<\/strong>.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Annular flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">Similar to vertical flow, at larger gas flow velocities, the liquid forms a continuous <strong>annular film on the channel wall<\/strong>. The horizontal annular flow is characterized by the presence of a <strong>thicker liquid film flowing on the bottom<\/strong> of the channel wall. The gas flows as a continuous phase in the center of the tube. The flow core can contain entrained liquid droplets. The velocity of the gas core is very large, and it is large enough to cause high-frequency waves and ripples at the interface. This flow regime is particularly stable, and it is desired flow regime for high-velocity, high-quality two-phase fluid flow.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Mist flow<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Mist flow<\/strong> is a flow regime of two-phase gas-liquid flow. It occurs at very high flow rates and very high flow quality. This condition causes liquid film flowing on the channel wall to be thinned by the shear of the gas core on the interface until it becomes unstable and is destroyed. The flow core in the mist flow entrains all the liquid as droplets in the gas phase. Droplets may wet the tube wall, but this occurs intermittently and only locally. In the heated channel, the presence of a mist flow regime is accompanied with significantly <strong>higher wall temperatures<\/strong> and high fluctuation of wall temperatures.<\/div><\/div>\n<figure id=\"attachment_14790\" aria-describedby=\"caption-attachment-14790\" style=\"width: 290px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Plug-Annular-Stratified-Mist-Wavy.png\"><img loading=\"lazy\" class=\"wp-image-14790 size-medium\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Plug-Annular-Stratified-Mist-Wavy-300x252.png\" alt=\"bubble, plug, slug, annular, mist, stratified or wavy flow\" width=\"300\" height=\"252\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Plug-Annular-Stratified-Mist-Wavy-300x252.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Bubbly-Slug-Plug-Annular-Stratified-Mist-Wavy.png 523w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14790\" class=\"wp-caption-text\">Sketches of flow regimes for two-phase flow in a horizontal pipe. Source: Weisman, J. Two-phase flow patterns. Chapter 15 in Handbook of Fluids in Motion, Cheremisinoff N.P., Gupta R. 1983, Ann Arbor Science Publishers.<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_14789\" aria-describedby=\"caption-attachment-14789\" style=\"width: 426px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-horizontal-flow.png\"><img loading=\"lazy\" class=\"wp-image-14789 size-full\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-horizontal-flow.png\" alt=\"flow patterns - horizontal flow\" width=\"436\" height=\"416\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-horizontal-flow.png 436w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-horizontal-flow-300x286.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/flow-patterns-horizontal-flow-52x50.png 52w\" sizes=\"(max-width: 436px) 100vw, 436px\" \/><\/a><figcaption id=\"caption-attachment-14789\" class=\"wp-caption-text\">A flow regime map for the flow of an air\/water mixture in a horizontal, 2.5cm diameter pipe at 25\u25e6C and 1bar. Solid lines and points are experimental observations of the transition conditions, while the hatched zones represent theoretical predictions. Source: Mandhane, J.M., Gregory, G.A. and Aziz, K.A. (1974). A flow pattern map for gas-liquid flow in horizontal pipes. Int. J. Multiphase Flow<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<h2>Flow patterns during evaporation<\/h2>\n<p>The previous section describes various <strong>flow patterns<\/strong> and shortly describes their behavior. These flow patterns were considered to be <strong>at constant void fraction<\/strong> and <strong>constant superficial velocities<\/strong>. But many industrial applications have to consider a <strong>variable void fraction<\/strong> and variable superficial velocities. In the nuclear industry, we have to deal with flow patterns during <strong>evaporation<\/strong> (i.e., during changes in the <a title=\"Void Fraction \u2013 Two-phase Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/void-fraction-two-phase-flow\/\">void fraction<\/a>).<\/p>\n<p>Detailed knowledge of <strong>phase changes<\/strong> and the behavior of the flow during the phase change is one of the most important considerations in the design of a <a title=\"Nuclear Reactor\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor\/\"><strong>nuclear reactor<\/strong><\/a>, especially in the following applications:<\/p>\n<ul>\n<li><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-14854\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig.png\" alt=\"convective evaporation - vertical channel\" width=\"262\" height=\"633\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig.png 262w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig-124x300.png 124w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><\/a><a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\">BWR &#8211; Boiling Water Reactors<\/a>\n<ul>\n<li>A <strong>boiling water reactor<\/strong> is cooled and <a title=\"Neutron Moderator\" href=\"http:\/\/sitepourvtc.com\/neutron-moderator\/\">moderated<\/a> by water like a PWR, but at a<strong> lower pressure<\/strong> (7MPa), which allows the water to <strong>boil inside the pressure vessel<\/strong> producing the steam that runs the turbines. Evaporation, therefore, occurs directly in fuel channels. Therefore, BWRs are the best example for this area because coolant evaporation occurs at normal operation and is a very desired phenomenon.<\/li>\n<li>In BWRs, there is a phenomenon that is of the <strong>highest importance in reactor safety<\/strong>. This phenomenon is known as the <strong>\u201cdry out\u201d<\/strong> and is directly associated with <strong>changes in flow pattern<\/strong> during evaporation. At normal, the fuel surface is effectively cooled by boiling coolant. However, when the heat flux exceeds a <strong>critical value <\/strong>(CHF &#8211; critical heat flux), the flow pattern may reach the <strong>dry-out conditions<\/strong> (a thin film of liquid disappears). The heat transfer from the fuel surface into the coolant is deteriorated due to a <strong>drastically increased fuel surface temperature<\/strong>.<\/li>\n<\/ul>\n<\/li>\n<li><a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWR &#8211; Pressurized Water Reactors<\/a>\n<ul>\n<li>In <strong>PWRs<\/strong> at <strong>normal operation,<\/strong> the flow is considered to be single-phase. But a great deal of study has been performed on the nature of <strong>two-phase flow<\/strong> in case of <strong>transients and accidents<\/strong> (such as the<strong> loss-of-coolant accident &#8211; LOCA or trip of RCPs<\/strong>), which are of importance in reactor safety and in must be proved and declared in the <strong>Safety Analysis Report<\/strong> (SAR). In the case of PWRs, the problematic phenomenon is not the dry out. In the case of PWRs, the critical flow is an <strong>inverted annular flow<\/strong>. This flow occurs when a\u00a0fuel rod cladding surface is overheated, which causes the formation of a<strong> local vapor layer<\/strong>, causing a dramatic reduction in heat transfer capability. This phenomenon is known as a <strong>departure from nucleate boiling &#8211; DNB<\/strong>. The difference in flow regime between post-dry outflow and post-DNB flow is depicted in the figure.<\/li>\n<li>In PWRs, evaporation also occurs in steam generators. Steam generators are <strong>heat exchangers<\/strong> that convert <strong>feedwater into steam<\/strong> from heat produced in a <a href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">nuclear reactor core<\/a>. The steam produced drives the turbine.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Difference in the flow regime: Dryout vs. DNB<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14862\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min.png\" alt=\"Dryout vs. DNB\" width=\"683\" height=\"911\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min.png 683w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Dryout-DNB-min-225x300.png 225w\" sizes=\"(max-width: 683px) 100vw, 683px\" \/><\/a><\/div><\/div><\/div><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14855\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig.png\" alt=\"convective evaporation - horizontal channel\" width=\"587\" height=\"226\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig.png 587w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig-300x116.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/a><div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Convective Evaporation - Vertical Channel<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-14854\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig.png\" alt=\"convective evaporation - vertical channel\" width=\"262\" height=\"633\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig.png 262w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-vertical-channel-fig-124x300.png 124w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><\/a><strong>Convective evaporation in a vertical channel<\/strong> is depicted in the figure. This figure shows the typical order of the flow regimes encountered from inlet to outlet of a <strong>heated channel<\/strong>. At the inlet, the <strong>liquid enters subcooled<\/strong> (at a lower temperature than saturation). In this region, the flow is single-phase. As the liquid heats up, the wall temperature correspondingly rises. As the <strong>wall temperature exceeds the saturation temperature<\/strong> (e.g.,, 285\u00b0C at 6.8 MPa), <strong>subcooled boiling begins<\/strong>. Bubbles nucleate in the superheated thermal <a title=\"Boundary Layer\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/boundary-layer\/\">boundary layer<\/a> on the heated wall but tend to <strong>condense in the subcooled bulk<\/strong>.<\/p>\n<p>Further increase in liquid temperature causes that the liquid bulk reaches its <strong>saturation temperature,<\/strong> and the convective boiling process passes through the <strong>bubbly flow<\/strong> into the <strong>slug flow<\/strong>. Increasing void fraction causes that the structure of the flow becomes unstable. The boiling process passes through the <strong>slug and churns flow<\/strong> into the <strong>annular flow regime<\/strong> with its characteristic annular film of the liquid. At given combinations of flow rate through a channel, pressure, flow quality, and linear heat rate, the <strong>liquid wall film may exhaust,<\/strong> and the wall may be <strong>dried out<\/strong>. At the dry-out point, the wall temperature significantly rises to dissipate the applied heat flux. The post-dry outflow (mist or drop flow) in the heated channel is undesirable because the presence of such a flow regime is accompanied with significantly higher wall temperatures and high fluctuation of wall temperatures.<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Convective Evaporation - Horizontal Channel<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><span style=\"font-weight: 400;\"><strong>Convective evaporation in a horizontal channel<\/strong> is very similar to the evaporation in the vertical channel. But <\/span><span style=\"font-weight: 400;\">for the horizontal channel, gravitational force tends to drain the liquid toward the bottom of the channel, and the vapor phase concentrates at the channel\u2019s top. Typical flow regimes, including cross-sectional views of the flow structure, are<\/span><span style=\"font-weight: 400;\"> depicted in the figure below. <\/span><\/p>\n<p><strong><span style=\"font-weight: 400;\">At the inlet, the <strong>liquid enters subcooled<\/strong> (at a lower temperature than saturation). In this region, the flow is single-phase. As the liquid heats up, the wall temperature correspondingly rises. As the wall temperature exceeds the <strong>saturation temperature<\/strong> (e.g.,, 285\u00b0C at 6.8 MPa), <strong>subcooled boiling begins<\/strong>. The convective boiling process passes through <strong>bubbly, plug regimes,<\/strong> and flow can be either <strong>stratified or unstratified<\/strong> (depending on the flow velocity). As can be seen, the channel dries out occurs at the top of the tube, where the film thickness is thinner due to gravitational force. Dryout then progresses around the perimeter from top to bottom along the channel. <\/span><\/strong><\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14855\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig.png\" alt=\"convective evaporation - horizontal channel\" width=\"587\" height=\"226\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig.png 587w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/convective-evaporation-horizontal-channel-fig-300x116.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/a><\/div><\/div><\/div>\n<h2>Two-phase Pressure Drop<\/h2>\n<p>In the practical analysis of piping systems, the quantity of most importance is the <strong>pressure loss due to viscous effects<\/strong> along the length of the system, as well as <strong>additional pressure losses<\/strong> arising from other <strong>technological equipments<\/strong> like valves, elbows, piping entrances, fittings, and tees.<\/p>\n<p>In contrast, to single-phase pressure drops, calculation and prediction of two-phase pressure drops is a much more complex problem, and leading methods differ significantly. Experimental data indicates that the <strong>frictional pressure drop in the two-phase flow<\/strong> (e.g.,, in a boiling channel) is <strong>substantially higher<\/strong> than for a single-phase flow with the same length and mass flow rate. Explanations include an apparently increased surface roughness due to bubble formation on the heated surface and increased flow velocities.<\/p>\n<h2>Pressure Drop &#8211; Homogeneous Flow Model<\/h2>\n<p>The simplest approach to predicting two-phase flows is to treat the entire two-phase flow as if it were <strong>all liquid<\/strong>, except flowing at the two-phase <strong>mixture velocity<\/strong>. The two-phase pressure drops for flows inside pipes and channels are the sum of three contributions:<\/p>\n<ul>\n<li>the static pressure drop <strong>\u2206p<sub>static<\/sub> <\/strong>(<a title=\"Elevation Head\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/elevation-head-2\/\">elevation head<\/a>)<\/li>\n<li>the momentum pressure drop <strong>\u2206p<sub>mom<\/sub><\/strong> (<a title=\"Fluid Acceleration \u2013 Pressure Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/minor-head-loss-local-losses\/fluid-acceleration-pressure-loss\/\">fluid acceleration<\/a>)<\/li>\n<li>the frictional pressure drop <strong>\u2206p<sub>frict<\/sub><\/strong><\/li>\n<\/ul>\n<p>The total pressure drop of the two-phase flow is then:<\/p>\n<p><strong>\u2206p<sub>total<\/sub> = \u2206p<sub>static<\/sub> + \u2206p<sub>mom<\/sub> + \u2206p<sub>frict<\/sub><\/strong><\/p>\n<p>The static and momentum pressure drops can be calculated similarly as in the case of single-phase flow and using the homogeneous <a title=\"Mixture Density \u2013 Two-phase Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/mixture-density-two-phase-flow\/\">mixture density<\/a>:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14774\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition.png\" alt=\"mixture density - definition\" width=\"312\" height=\"51\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition.png 312w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/mixture-density-definition-300x49.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/a><\/p>\n<p>The most problematic term is the<strong> frictional pressure drop<\/strong> <strong>\u2206p<sub>frict<\/sub><\/strong>, which is based on the single-phase pressure drop multiplied by the <strong>two-phase correction factor<\/strong> (<strong>homogeneous friction multiplier &#8211; \u03a6<sub>lo<\/sub><sup>2<\/sup><\/strong>). By this approach, the frictional component of the two-phase pressure drop is:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-pressure-drop-equation.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14901\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-pressure-drop-equation.png\" alt=\"two-phase pressure drop - equation\" width=\"225\" height=\"68\" \/><\/a><\/p>\n<p>where <strong>(dP\/dz)<sub>2f<\/sub><\/strong>\u00a0is frictional pressure gradient of two-phase flow and <strong>(dP\/dz)<sub>1f<\/sub><\/strong> is frictional pressure gradient if an entire flow (of total mass flow rate G) flows like a liquid in the channel (<a title=\"Major Head Loss \u2013 Friction Loss\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/\">standard single-phase pressure drop<\/a>).\u00a0The term<strong> \u03a6<sub>lo<\/sub><sup>2\u00a0<\/sup><\/strong>is the <strong>homogeneous friction multiplier<\/strong> that can be derived according to various methods. One of the possible multipliers is\u00a0equal to <strong>\u03a6<sub>lo<\/sub><sup>2<\/sup>\u00a0=\u00a0(1+x<sub>g<\/sub>(\u03c1<sub>l<\/sub>\/\u03c1<sub>g<\/sub> &#8211; 1))<span style=\"font-weight: 400;\"><strong>\u00a0<\/strong>and therefore:<\/span><\/strong><br \/>\n<a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-pressure-drop-equation2.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14902\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-pressure-drop-equation2.png\" alt=\"two-phase pressure drop - equation2\" width=\"369\" height=\"78\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-pressure-drop-equation2.png 369w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/two-phase-pressure-drop-equation2-300x63.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/a><\/p>\n<p>As can be seen, this simple model suggests that the <strong>two-phase frictional losses are in any event higher than the single-phase frictional losses.<\/strong> The homogeneous friction multiplier increases rapidly with <a title=\"Static Quality \u2013 Flow Quality\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/static-quality-flow-quality\/\"><strong>flow quality<\/strong><\/a>.<\/p>\n<p>Typical<strong> flow qualities<\/strong> in<a title=\"Steam Generator\" href=\"http:\/\/sitepourvtc.com\/steam-generator\/\"><strong> steam generators<\/strong><\/a> and <a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\"><strong>BWR cores<\/strong><\/a> are on the order of 10 to 20 %. The corresponding two-phase frictional loss would be<strong> 2 &#8211; 4<\/strong> times that in an equivalent single-phase system.<\/p>\n<div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Martinelli-Nelson Friction Multiplicator<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_14903\" aria-describedby=\"caption-attachment-14903\" style=\"width: 551px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Martinelli-Nelson-frictional-pressure-drop.png\"><img loading=\"lazy\" class=\"size-full wp-image-14903\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Martinelli-Nelson-frictional-pressure-drop.png\" alt=\"Martinelli-Nelson frictional pressure drop\" width=\"561\" height=\"497\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Martinelli-Nelson-frictional-pressure-drop.png 561w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Martinelli-Nelson-frictional-pressure-drop-300x266.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/a><figcaption id=\"caption-attachment-14903\" class=\"wp-caption-text\">The Martinelli-Nelson frictional pressure drop function for water depends on the prevailing pressure level and the mass exit quality.<br \/>Source: http:\/\/authors.library.caltech.edu\/25021\/1\/chap8.pdf<\/figcaption><\/figure>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Separated-phases flow model - Lockhart-Martinelli correlation<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">An alternate approach to calculate two-phase pressure drop is <strong>the separated-phases model.<\/strong><\/p>\n<p>In this model, the <strong>phases<\/strong> are considered to be flowing <strong>separately<\/strong> in the channel, each occupying a <strong>given fraction<\/strong> of the channel cross-section and each with a <strong>given velocity<\/strong>. It is obvious the predicting the<a title=\"Void Fraction \u2013 Two-phase Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/void-fraction-two-phase-flow\/\"><strong> void fraction<\/strong><\/a> is very important for these methods. Numerous methods are available for predicting the void fraction.<\/p>\n<p>The method of <strong>Lockhart and Martinelli<\/strong> is the original method that predicted the <strong>two-phase frictional pressure drop<\/strong> based on a friction multiplicator for the <strong>liquid-phase or the vapor-phase<\/strong>:<\/p>\n<p><strong>\u2206p<sub>frict<\/sub> = \u03a6<sub>ltt<\/sub><sup>2<\/sup> . \u2206p<sub>l<\/sub><\/strong> (liquid-phase \u2206p)<\/p>\n<p><strong>\u2206p<sub>frict<\/sub> = \u03a6<sub>gtt<\/sub><sup>2<\/sup> . \u2206p<sub>g<\/sub><\/strong> (vapor-phase \u2206p)<\/p>\n<p>The single-phase friction factors of the liquid <strong>f<sub>l<\/sub> <\/strong>and the vapor <strong>f<sub>g<\/sub><\/strong> are <a title=\"Darcy Friction Factor\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/darcy-friction-factor-2\/\">based on the single-phase<\/a> flowing alone in the channel, in either <a title=\"Laminar Flow \u2013 Viscous Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/laminar-flow-viscous\/\">viscous laminar<\/a> (v) or <a title=\"Turbulent Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/turbulent-flow\/\">turbulent<\/a> (t) regimes.<\/p>\n<p><strong>\u2206p<sub>l<\/sub><\/strong> can be calculated classically but with the application of <strong>(1-x)<sup>2<\/sup><\/strong> in the expression and <strong>\u2206p<sub>g<\/sub><\/strong> with the application of vapor quality <strong>x<sup>2,<\/sup><\/strong> respectively.<\/p>\n<p>The two-phase multipliers <strong>\u03a6<sub>ltt<\/sub><sup>2<\/sup><\/strong> and <strong>\u03a6<sub>gtt<\/sub><sup>2<\/sup> <\/strong>are equal to:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Lockhart-Martinelli-multipliers.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14904\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Lockhart-Martinelli-multipliers.png\" alt=\"Lockhart-Martinelli - multipliers\" width=\"286\" height=\"112\" \/><\/a><\/p>\n<p>where<strong> X<sub>tt<\/sub> <\/strong>is the <strong>Martinelli\u2019s parameter<\/strong> defined as:<\/p>\n<p><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Martinelli-parameter.png\"><img loading=\"lazy\" class=\"aligncenter size-full wp-image-14905\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Martinelli-parameter.png\" alt=\"Martinelli parameter\" width=\"235\" height=\"68\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Lockhart-Martinelli-table.png\"><img loading=\"lazy\" class=\"alignright size-full wp-image-14906\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Lockhart-Martinelli-table.png\" alt=\"Lockhart-Martinelli - table\" width=\"250\" height=\"124\" \/><\/a>and the value of <strong>C<\/strong> in these equations depends on the <a title=\"Flow Regime\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/flow-regime\/\">flow regimes<\/a> of the liquid and vapor.\u00a0<\/span>These values are in the following table.<\/p>\n<p><strong><span style=\"font-weight: 400;\"><strong>The Lockhart-Martinelli correlation<\/strong> is adequate for two-phase flows at low and moderate pressures. Martinelli and Nelson\u2019s (1948) and Thom (1964) revised models are recommended for applications at higher pressures.<\/span><\/strong><\/p>\n<figure id=\"attachment_14907\" aria-describedby=\"caption-attachment-14907\" style=\"width: 502px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/separated-flow-model-Lockhart-Martinelli-correlation.png\"><img loading=\"lazy\" class=\"size-full wp-image-14907\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/separated-flow-model-Lockhart-Martinelli-correlation.png\" alt=\"separated flow model - Lockhart-Martinelli correlation\" width=\"512\" height=\"482\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/separated-flow-model-Lockhart-Martinelli-correlation.png 512w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/separated-flow-model-Lockhart-Martinelli-correlation-300x282.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/separated-flow-model-Lockhart-Martinelli-correlation-52x50.png 52w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/a><figcaption id=\"caption-attachment-14907\" class=\"wp-caption-text\">Correlations for void fraction and frictional pressure drop (Lockhart and Martinelli, 1949)<\/figcaption><\/figure>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>Example: Pressure Drop - BWR<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">\n<figure id=\"attachment_14915\" aria-describedby=\"caption-attachment-14915\" style=\"width: 587px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Pressure-Drop-BWR.png\"><img loading=\"lazy\" class=\"size-full wp-image-14915\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Pressure-Drop-BWR.png\" alt=\"Pressure Drop - BWR\" width=\"597\" height=\"641\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Pressure-Drop-BWR.png 597w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/06\/Pressure-Drop-BWR-279x300.png 279w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/a><figcaption id=\"caption-attachment-14915\" class=\"wp-caption-text\">Source: http:\/\/www.nrc.gov\/docs\/ML1214\/ML12142A157.pdf<\/figcaption><\/figure>\n<\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span> Two-phase Minor Loss<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\">In industry, any pipe system contains different technological elements as b<strong>ends, fittings, valves, or heated channels<\/strong>. These additional components add to the overall head loss of the system. Such losses are generally termed <strong>minor losses<\/strong>, although they often account for a major portion of the <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/bernoullis-equation-bernoullis-principle\/head-loss\/\">head loss<\/a>. For relatively short pipe systems, with a relatively large number of bends and fittings,<strong> minor losses can easily exceed<\/strong> <a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/major-head-loss-friction-loss\/\">major losses<\/a> (especially with a partially closed valve that can cause a greater pressure loss than a long pipe when a valve is closed or nearly closed, the minor loss is infinite).<\/p>\n<p>Single-phase minor losses are commonly measured experimentally. The data, especially for valves, are somewhat dependent upon the particular manufacturer\u2019s design. <strong>The two-phase pressure loss<\/strong> due to local flow obstructions is treated in a <strong>manner similar to the single-phase frictional losses<\/strong> &#8211; <strong>via local loss multiplier<\/strong>.<\/p>\n<p>See more: <a href=\"http:\/\/www.nrc.gov\/docs\/ML0613\/ML061380693.pdf\" class=\"broken_link\">TWO-PHASE FRICTIONAL PRESSURE LOSS IN HORIZONTAL BUBBLY FLOW WITH 90-DEGREE BEND\u00a0<\/a><\/div><\/div><\/div>\n<h2>Flow Instability<\/h2>\n<p>In general, there are <strong>many\u00a0instabilities<\/strong> that may occur in <strong>two-phase systems<\/strong>. In <a title=\"Nuclear Engineering\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/\">nuclear engineering<\/a>, the study of the <strong>multiphase flow stability<\/strong> is important in the <strong>accident management<\/strong> of <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">pressurized water reactors<\/a> and the <strong>highest importance<\/strong> in <strong>normal\/abnormal conditions<\/strong> in <a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\">boiling water reactors<\/a>.<\/p>\n<p>In <strong>PWRs<\/strong> at <strong>normal operation,<\/strong> the flow is considered to be single-phase. But a great deal of study has been performed on the flow instability in case of <strong>transients and accidents <\/strong>(such as the<strong> loss-of-coolant accident \u2013 LOCA or trip of RCPs with the presence of natural circulation<\/strong>)<strong>,<\/strong> in which flow oscillations or flow reversals may occur.<\/p>\n<p>Flow oscillations are variations in flow caused by void formations, which are undesirable for several reasons.<\/p>\n<ul>\n<li>Flow oscillations can cause <strong>undesirable mechanical stress<\/strong> on fuel components (such as spacing grids). This can lead to the failure of those components due to fatigue.<\/li>\n<li>Flow oscillations affect the <strong>local heat transfer<\/strong> characteristics. In the case of <a title=\"PWR \u2013 Pressurized water reactor\" href=\"http:\/\/sitepourvtc.com\/pwr-pressurized-water-reactor\/\">PWRs<\/a>, the critical safety issue is named <strong>DNB<\/strong> (<strong>departure from nucleate boiling<\/strong>), which causes the formation of a<strong> local vapor layer<\/strong>, causing a dramatic reduction in heat transfer capability. It has been found through testing that the <strong>critical heat flux (CHF)<\/strong> required for departure from nucleate boiling (DNB) can be lowered by as much as 40% when the flow is oscillating. This severely reduces the <strong>thermal limit<\/strong> and the power density along the length of the <a title=\"Reactor Core\" href=\"http:\/\/sitepourvtc.com\/nuclear-power-plant\/nuclear-reactor-core\/\">reactor core<\/a>.<\/li>\n<\/ul>\n<p>Flow oscillations can be a problem during <strong>natural circulation<\/strong> operations (e.g.,, after tripping of all RCPs). <strong>Natural circulation<\/strong> is an important design feature and ultimate heat removal mechanism. Because of the low flow rates present, coolant boiling may occur, which may form flow oscillations. During natural circulation, the steam bubbles formed during a flow oscillation may have enough effect to actually cause complete flow reversal in the affected channel.<\/p>\n<figure id=\"attachment_14932\" aria-describedby=\"caption-attachment-14932\" style=\"width: 290px\" class=\"wp-caption alignright\"><a href=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/07\/BWR-flow-instability.png\"><img loading=\"lazy\" class=\"size-medium wp-image-14932\" src=\"http:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/07\/BWR-flow-instability-300x177.png\" alt=\"BWR - flow instability\" width=\"300\" height=\"177\" srcset=\"https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/07\/BWR-flow-instability-300x177.png 300w, https:\/\/sitepourvtc.com\/wp-content\/uploads\/2016\/07\/BWR-flow-instability.png 794w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/a><figcaption id=\"caption-attachment-14932\" class=\"wp-caption-text\">Instability Region in the Power-Flow Map for BWR reactor. Source: Francesco D\u2019Auria, The BWR Stability Issue, THICKET 2008 \u2013 Session IX \u2013 Paper 26<\/figcaption><\/figure>\n<p><strong>In <a title=\"BWR \u2013 Boiling water reactor\" href=\"http:\/\/sitepourvtc.com\/bwr-boiling-water-reactor\/\">BWRs<\/a>,<\/strong> evaporation of coolant occurs at <strong>normal operation,<\/strong> and it is a very desired phenomenon. On the other hand, convective evaporation in the fuel channel causes that the <a title=\"Flow Patterns \u2013 Two-phase Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/flow-patterns-two-phase-flow\/\">flow pattern<\/a> changes along the fuel channel depending on the flow rate and thermal power. It has been found that there are <strong>instability regions<\/strong> in which two-phase flow instabilities may arise. These two-phase flow instabilities are undesirable as they can result in mechanical vibrations and system control problems, affect normal operation, restrict operating parameters, and influence reactor safety. It must be noted flow stability in BWRs is not a major issue for many years because it is a well-known phenomenon.<\/p>\n<p>In general, there are many classifications of flow instabilities. The following classification is based upon thermal-hydraulic fundamental mechanisms:<\/p>\n<p><strong>The static instabilities<\/strong> are:<\/p>\n<ul>\n<li><strong>Flow excursion<\/strong><\/li>\n<li><strong>Boiling crisis<\/strong><\/li>\n<li><strong>Relaxation types, including flow pattern transition<\/strong><\/li>\n<\/ul>\n<p><strong>The dynamic instabilities<\/strong> are:<\/p>\n<ul>\n<li><strong>Density wave oscillations<\/strong><\/li>\n<li><strong>Pressure drop oscillations<\/strong><\/li>\n<li><strong>Thermal oscillations<\/strong>.<\/li>\n<\/ul>\n<p>The proper characterization of the instabilities and the condition for their occurrence can determine the optimal and safe operation of the systems. The most accepted explanation for the occurrence of the dynamic type of instabilities is called <strong>density wave oscillations (DWO)<\/strong>.<\/p>\n<p><strong>The density wave<\/strong> causes a delay in the<strong> local pressure drop<\/strong> caused by a change in inlet flow. Because of this delay, the sum of all local pressure drops may result in a total drop that is <strong>out-of-phase<\/strong> with the inlet flow. The basic mechanism causing flow instabilities in BWRs is the density wave. The characteristic periods of these oscillations are associated with the time required for a fluid particle to travel through the entire loop.<\/p>\n<p>Types of instabilities observed in BWRs<\/p>\n<ul>\n<li><strong>Control System Instabilities.<\/strong> Control system instabilities are related to the action of controllers that, through actuators, attempt to regulate some of the variables of the reactor.<\/li>\n<li><strong>Channel Flow Instabilities.<\/strong> This type of instability can be described as follows: Let assume a flow perturbation. This perturbation causes a \u201cwave\u201d of voids traveling upward through the channel, producing a two-phase pressure drop (pressure drop increases significantly as void fraction increases) that is delayed with respect to the original perturbation. An increase in channel pressure drop (density wave) \u00a0may lead to instability in the flow rate.<\/li>\n<li><strong>Coupled Neutronic-Thermohydraulic Instability.<\/strong> The dominant type of instabilities in commercial BWRs is the coupled neutronic-thermohydraulic instability (also known as <strong>reactivity instability<\/strong>). The power generation in BWRs is directly related to the fuel <a title=\"Neutron Flux Density \u2013 Neutron Intensity\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-engineering-fundamentals\/neutron-nuclear-reactions\/neutron-flux-neutron-intensity\/\"><strong>neutron flux<\/strong><\/a>, which is strongly related to the average <a title=\"Void Fraction \u2013 Two-phase Flow\" href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/void-fraction-two-phase-flow\/\"><strong>void fraction<\/strong><\/a> in the core channels. This effect is known as <a title=\"Reactivity Coefficients \u2013 Reactivity Feedbacks\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/\"><strong>reactivity feedback<\/strong><\/a>. The reactivity feedback caused by changes in void fraction (<a title=\"Void Coefficient\" href=\"http:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/reactivity-coefficients-reactivity-feedbacks\/void-coefficient\/\">void coefficient<\/a>) is delayed as the voids travel upward through the fuel channel. In some cases, the delay may be long enough, and the <strong>void feedback<\/strong> may be strong enough that the reactor configuration becomes unstable. In this case, the neutron flux may oscillate.<\/li>\n<\/ul>\n<p>Special References:<\/p>\n<ul>\n<li>Francesco D\u2019Auria, The BWR Stability Issue, THICKET 2008 \u2013 Session IX \u2013 Paper 26<\/li>\n<li>Dag Str\u00f8msv\u00e5g,\u00a0Fundamental mechanisms of density wave oscillations and the effect of subcooling, NTNU, 2011.<\/li>\n<li>J. March-Leuba,\u00a0Density -Wave Instabilities in Boiling Water Reactors.\u00a0NUREG\/CR-6003, ORNL, 1992.<\/li>\n<\/ul>\n<\/div>\n<div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:20px 0;border-width:2px;border-color:#999999\"><\/div>\n<div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-100 lgc-tablet-grid-100 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\u00a0 <div   id="8n9s8rpp6h"    class=\"su-accordion su-u-trim\"><div   id="8n9s8rpp6h"    class=\"su-spoiler su-spoiler-style-default su-spoiler-icon-plus su-spoiler-closed\" data-scroll-offset=\"0\"><div   id="8n9s8rpp6h"    class=\"su-spoiler-title\" tabindex=\"0\" role=\"button\"><span class=\"su-spoiler-icon\"><\/span>References:<\/div><div   id="8n9s8rpp6h"    class=\"su-spoiler-content su-u-clearfix su-u-trim\"><strong>Reactor Physics and Thermal Hydraulics:<\/strong>\n<ol>\n<li>J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading,\u00a0MA (1983).<\/li>\n<li>J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.<\/li>\n<li>W. M. Stacey, Nuclear Reactor Physics, John Wiley &amp; Sons, 2001, ISBN: 0- 471-39127-1.<\/li>\n<li>Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering,\u00a0Springer; 4th edition, 1994, ISBN:\u00a0978-0412985317<\/li>\n<li>Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC\u00a0Press; 2\u00a0edition, 2012, ISBN:\u00a0978-0415802871<\/li>\n<li>Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN:\u00a0978-3-319-13419-2<\/li>\n<li>Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition,\u00a0John Wiley &amp; Sons, 2006, ISBN:\u00a0978-0-470-03037-0<\/li>\n<li>Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010,\u00a0ISBN 978-1-4020-8670-0.<\/li>\n<li>U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER,\u00a0AND FLUID FLOW.\u00a0DOE Fundamentals Handbook,\u00a0Volume 1, 2 and 3. June\u00a01992.<\/li>\n<li>White Frank M., Fluid Mechanics, McGraw-Hill Education, 7th edition, February, 2010, ISBN:\u00a0978-0077422417<\/li>\n<\/ol>\n<\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-dotted\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><\/div><\/div><div   id="8n9s8rpp6h"    class=\"su-divider su-divider-style-default\" style=\"margin:15px 0;border-width:2px;border-color:#999999\"><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\">\n<h2>See above:<\/h2>\n<p>Fluid Dynamics<a href=\"http:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\" class=\"su-button su-button-style-flat\" style=\"color:#606060;background-color:#ffffff;border-color:#cccccc;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px\" target=\"_self\"><span style=\"color:#606060;padding:7px 20px;font-size:16px;line-height:24px;border-color:#ffffff;border-radius:10px;-moz-border-radius:10px;-webkit-border-radius:10px;text-shadow:0px 0px 0px #000000;-moz-text-shadow:0px 0px 0px #000000;-webkit-text-shadow:0px 0px 0px #000000\"><i class=\"sui sui-link\" style=\"font-size:16px;color:#5d5d5d\"><\/i> <\/span><\/a><\/p><\/div><\/div><div   id="8n9s8rpp6h"     class=\"lgc-column lgc-grid-parent lgc-grid-33 lgc-tablet-grid-33 lgc-mobile-grid-100 lgc-equal-heights \"><div   id="8n9s8rpp6h"     class=\"inside-grid-column\"><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>By definition, multiphase flow is the interactive flow of two or more distinct phases with common interfaces in, say, a conduit. Each phase, representing a volume fraction (or mass fraction) of solid, liquid, or ga搜索引擎优化us matter, has its own properties, velocity, and temperature. A multiphase flow can be a simultaneous flow of: Materials with different &#8230; <a title=\"Two-phase Fluid Flow\" class=\"read-more\" href=\"https:\/\/sitepourvtc.com\/nuclear-engineering\/fluid-dynamics\/two-phase-fluid-flow\/\" aria-label=\"More on Two-phase Fluid Flow\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":14182,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"generate_page_header":""},"_links":{"self":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14763"}],"collection":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/comments?post=14763"}],"version-history":[{"count":4,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14763\/revisions"}],"predecessor-version":[{"id":33094,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14763\/revisions\/33094"}],"up":[{"embeddable":true,"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/pages\/14182"}],"wp:attachment":[{"href":"https:\/\/sitepourvtc.com\/wp-json\/wp\/v2\/media?parent=14763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}